On Landsberg Unicorns of General $(α,β)$-Type

In this paper, we investigate the classes of \lq\lq unicorns" of general $(α,β)$-metric types, namely, Landsberg general $(α,β)$-metrics that are non-Berwaldian. We provide explicit solutions for these metrics, including several new classes. Furthermore, we identify and exclude the cases that yield degenerate metrics to guarantee the geometric validity of the established solutions.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-10-27
DOI
https://doi.org/10.48550/arxiv.2610.37241
Primary Topic
Advanced Differential Geometry Research
Type
preprint
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preprint

On Landsberg Unicorns of General $(α,β)$-Type

Salah Gomaa Elgendi
arXiv (Cornell University)
Advanced Differential Geometry Research
preprint

On Landsberg Unicorns of General $(α,β)$-Type

Salah Gomaa Elgendi
preprint en

Abstract

In this paper, we investigate the classes of \lq\lq unicorns" of general $(α,β)$-metric types, namely, Landsberg general $(α,β)$-metrics that are non-Berwaldian. We provide explicit solutions for these metrics, including several new classes. Furthermore, we identify and exclude the cases that yield degenerate metrics to guarantee the geometric validity of the established solutions.

arXiv (Cornell University)
Advanced Differential Geometry Research
DOIOpen Access PDFOpenAlex
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